Minimum of functional...

[eljose]

Let be F the functional given by

J(y)=J(x,y,dy/dx)

my question is,apart from the usual definition of functional derivative and Lagrange equation,..does a numerical method exist to calculate it,i mean am looking for a recursive method,you introduce an initial function y0(x) from this you get a function y1(x) and os on with the limit with n tending to infinty taht d(yn(x),yn+1(x))=0 as n tends to infintiy

[Crosson]

Yes it can be done, in the days before the tidy euler-lagrange equation we are presented with, Euler represented a functional as a regular function of infinitely many variables, and differentiated wrt to each variable to find a stationary point.